To provide the best experience for the most-used Linux versions, we will end support for Google Chrome on 32-bit Linux, Ubuntu Precise (12.04), and Debian 7 (wheezy) in early March, 2016. Chrome will continue to function on these platforms but will no longer receive updates and security fixes.

We intend to continue supporting the 32-bit build configurations on Linux to support building Chromium. If you are using Precise, we'd recommend that you to upgrade to Trusty.

The first signs of the end of 32bit are on the wall - starting with Linux. I wonder how long Google will continue to support 32bit Chrome on Windows. For some strange reason, Microsoft is still selling 32bit Windows 10.

Installing and running 32 bit x86 software on Alpha was already achieved by DEC with their FX!32 technology.
Then we had Itanium which did the same thing natively. On Linux ia64 systems and Itanium processors with x86 hardware emulation you can directly execute x86 binaries.

So there was plenty of experience, years before AMD came around and introduced their 64-bit architecture.

FX!32 on Alpha was a DEC creation, and used binary translation begin converting binaries before Windows' own loader was invoked. FX!32 apps called natively to Windows DLLs and the kernel.

As another poster pointed out, NT on Alpha was essentially 32-bit (Alpha itself didn't have a 32-bit mode, so I'm thinking it means Windows was using 32-bit pointers internally, and 32-bit integers in data structures), so this translation would've been relatively easy, since everything woudld've retained the same size (No need to modify code to start handling 64-bit integers instead of 32-bit, for example)

Windows also ran x86 on Itanium systems, using - you guessed it - WoW64, which was introduced with Windows Server 2003, which was also the first Windows with an x86-64.